244 



or 



Mr Greenhill, On the rotation of a [Mar. 24/ 



1 /- ^\ 1 „ /c^sn^acn'^a /snadna E „\ 



Fsnacna 1 E 1 „ \ r. 

 va k^K k^ J 



1c^ dn( 



If now an additional angular velocity &> be communicated to the 

 ellipsoid about the axis of z, then we shall have 



V = (0 -s — 7^ x+ ax, 



w = ; 



the axes of x and y rotating with angular velocity co -h &>', and the 

 dynamical equations 



Idp . du du du ^ 

 -^ + Ax + ^ + u^ + v^ = 0, 

 pox ot ox oy 



Idp -r, dv dv dv 



become 



smce 



Idp 



p da 

 du 



dt 



+ Cz 



= 0, 



dv „ a^-b\ , ,« 



8w _ ^^ _ J 



8a; ' dy ^ 



dv 

 dy 



= 0; 



8v 

 u,r-= ico' 



ox 



a'-h' 

 a' + ¥ 



— 0) 7 a;, 



a'^ + 6^ 



- ^ + -4ir — 2w (ft) + 0)') -^ — To a; + -! ft)"' 

 /o da; ^ a + 



/o dx 



Idp 

 pdy 



+ % + 2ft) (ft) + ft) )^5-^2 2/ + j&> 



7^2 _ JSv 2 I 





= 0. 



